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Home > APCALC > Chapter 10 > Lesson 10.3.1 > Problem 10-138

10-138.

Multiple Choice: A function that satisfies the differential equation $f^\prime(x) + f(x) = 0$ is:

$f(x) = \sin (x)$

$f(x) = \cos (x)$

$f(x) = e^x$

$f(x) = e^{−x}$

$f(x) = \ln (x)$

Step 1:

$\frac{dy}{dx}+y=0$

Step 2:

$dy=-ydx$

Step 3:

$\frac{dy}{y}=-dx$

Step 4:

$\text{Integrate: }\ln|y|=-x+C$

Step 5:

$y=Ce^{-x}$

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